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Sphere cooling by radiation in surroundings: cooling rate at a new temperature (Stefan's law)

The same question, asked 6 times: 4 May 2023 S1*, 12 May 2024 S2*, 21 Apr 2025 S2*, 17 Apr 2026 S1*, 20 Apr 2026 S1*, 20 Apr 2026 S2. Every wording below, oldest first.

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  1. Question 1

    4 May 2023 S1

    45
    A sphere is at temperature 600 K. In an external environment of 200 K, its cooling rate is R. When the temperature of the sphere falls to 400 K, then cooling rate R' will become

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  2. Question 2

    12 May 2024 S2

    19
    Compare the rate of loss of heat from a metal sphere at 627°C627°C with the rate of loss of heat from the same sphere at 327°C327°C, if the temperature of the surrounding is 27°C27°C (nearly)

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  3. Question 3

    21 Apr 2025 S2

    29
    If a black body at 400 K surrounded by atmosphere at 300 K has rate of cooling ' R0R_{0} ', the same body at 900 K , surrounded by same atmosphere, will have rate of cooling nearly

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  4. Question 4

    17 Apr 2026 S1

    112
    In an external environment of temperature (T)(T) kelvin, a sphere at temperature (3T)(3T) kelvin has cooling rate R1R_1. When the temperature of that sphere falls to (2T)(2T) kelvin, the cooling rate R2R_2 of the sphere will become

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  5. Question 5

    20 Apr 2026 S1

    112
    A sphere is at temperature 600600 K. In an external environment of 200200 K, its cooling rate is R. When the temperature of the sphere falls to 400400 K then cooling rate R' will become

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  6. Question 6

    20 Apr 2026 S2

    114
    A sphere having temperature 600 K is losing heat due to radiation. At this temperature its rate of cooling is RR. The rate of cooling of this sphere at 400 K is x243\dfrac{x}{243}. The value of xx is (Temperature of surrounding is 300 K)

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